Question

Subtract rational expression.
Show work please.

Answer 1

Given:

`$(x+4)/(x-1)-(5)/(x^(2)-1)`

To find:

The simplified rational expression by subtraction.

Solution:

Let us factor
`x^2-1`. It can be written as
`x^2-1^2`.

`x^2-1^2=(x-1)(x+1)` using algebraic identity.

`$(x+4)/(x-1)-(5)/(x^(2)-1)=(x+4)/(x-1)-(5)/((x+1)(x-1))`

LCM of
`x-1,(x+1)(x-1)=(x+1)(x-1)`

Make the denominators same using LCM.

Multiply and divide the first term by (x + 1) to make the denominator same.

`$=((x+4)(x+1))/((x-1)(x+1))-(5)/((x-1)(x+1))`

Now, denominators are same, you can subtract the fractions.

`$=((x+4)(x+1)-5)/((x-1)(x+1))`

Expand
`(x+4)(x+1)-5`.

`$=(x^2+4x+x+4-5)/((x-1)(x+1))`

`$=(x^(2)+5 x-1)/((x-1)(x+1))`

`$(x+4)/(x-1)-(5)/(x^(2)-1)=(x^(2)+5 x-1)/((x-1)(x+1))`